The so-called method of 14C (carbon-14 or radiocarbon), is a radiometric dating method based on the measurement of relative abundances of carbon isotopes. The method of 14C allows dating organic materials (bone, wood, textile fibers, seeds, wood, coals . . . ), thus containing carbon atoms.
Carbon is a chemical element essential to life and present in all organic substances. It is present on earth in three isotopes: two stable ones (12C and 13C) and a radioactive one (14C). The latter turns by beta decay into nitrogen (N—14), with an average half-life of 5730 years, thus this isotope would disappear in the long run, if not continually reinstated. The production of new 14C regularly occurs in nature in the high layers of the troposphere and in the stratosphere, by the capture of thermal neutrons, secondary components of cosmic rays, by the nitrogen atoms present in the atmosphere. The dynamic balance between production and radioactive decay then keeps the concentration of 14C in the atmosphere constant, where it is mainly bound to oxygen in the form of carbon dioxide.
All living organisms that are part of the carbon cycle are continuously exchanging carbon with the atmosphere through breathing (animals) or photosynthesis (plants) processes or they assimilate it by feeding on other living beings or organic substances. Consequently, until a body is alive, the isotopic ratio of 14C and that of the other two carbon isotopes remains constant and equal to what is found in the atmosphere. In particular, the current natural isotopic ratio (abundance) in the atmosphere is:
      r    0    =                                         14                ⁢        C            C        ≈          1.2      ×                        10                      -            12                          .            
After death, these processes end and the organism does not exchange carbon with the outside anymore. Then, as a result of decay, the isotopic ratio decreases on a regular basis according to the formula: r=r0e−Δt/τ, where Δt is the time elapsed from the death of the organism and τ is the average lifespan of 14C.
By measuring the amount of 14C present in organic remains, the age thereof is obtained by applying the following formula: Δt=−τ ln(c/c0).
The measurement of 14C is possible, given the low concentrations present, with the method of mass spectrometry (AMS, Accelerator Mass Spectrometry): using a mass spectrometer, the concentration of 14C present in the sample is measured. This method is able to obtain reliable measurements for concentrations in the order of
                             14            ⁢      C        C    ≈            10              -        15              .  
However, the costs related to AMS equipment are relevant, in the order of millions of euros, and the overall dimensions of the same equipment is substantial, with high operating voltages.
Additionally, the detection of trace gases is generally very relevant in various technology fields. Apart from dating, the measurement of the amount of radiocarbon is important in biomedicine or in environmental and earth science.
The conventional cavity ring-down (CRD) spectroscopic technique was devised over 20 years ago, using pulsed laser first and then continuous emission laser. The advantages of CRD are mainly two, as detailed below: the signal is immune to width fluctuations of the radiation source used, and the linear absorption coefficient is measured directly and then, knowing the total pressure of the gas and the line-strength of the spectroscopic transition, the concentration of the molecular species to be measured.
A class of techniques for measuring the concentration of a gas is spectroscopy. Spectroscopy is a scientific technique that analyzes the spectrum of electromagnetic radiation emitted by a source split in its wavelengths and hence it analyze the properties of atoms or molecules that are the source of such radiation. In these spectra, the lines of absorption or emission can be studied.
The origin of a given spectral line can be an electronic, vibrational or rotational transition of the molecule of interest. For example, in the infrared, the main origins of a spectral line are not transitions between energy levels of electrons, generally dominating in the visible spectrum, but transitions between molecular vibrational energy levels.
A typical CRDS spectroscopy includes an apparatus comprising a laser that is used to send a highly fine coherent radiation beam consisting for example of two highly reflective mirrors (for example with a R>99.9%). When the radiation emitted by the laser is in resonance with a cavity mode, the radiation intensity increases in the cavity due to constructive interference phenomena. The laser is then quickly switched off, or moved away from the resonance cavity, in order to measure the exponentially decreasing intensity of light that escapes from the cavity. During this decay, the light is reflected back and forth thousands of times by the mirrors giving an effective path along a few miles.
If a gas or a mixture of gases that absorb light is placed inside the cavity, the intensity of photons trapped decreases by a fixed percentage along each path inside the cavity due to the scattering and absorption by the medium in the cavity and due to reflectivity losses. The light intensity inside the cavity is then given by an exponential function of time: I(t)=I0 exp (−t/τ).
CRD spectroscopy measures how long τ (time) light employs for its intensity to decay to 1/e of its initial intensity value, and this value of ring-down time is used to calculate the concentration of the absorbing substance in the gas inside the cavity.
The operating principle is thus based on the extent of a decay rate rather than an absolute absorbance. The decay constant τ is called “ring-down” and is dependent on loss mechanisms inside the cavity. For an empty cavity, i.e. without an absorbing medium inside, the decay constant τ0 is dependent on mirror losses (transmission, absorption and scattering) and various optical phenomena such as diffraction:
            τ      0        =                  n        c            ·              l                  1          -          R          +          X                      ,where n is the refractive index of the medium in the cavity, c the speed of light in vacuum, l is the length of the cavity, R the reflectivity of the mirrors, and X takes into account various other optical losses. The equation uses the ln(1+y)≈y approximation for y close to zero, which is the case in the working conditions of the CRD.
A gas inside the cavity absorbs energy by increasing the losses according to the Beer-Lambert law and then the intensity decays more quickly. Therefore, assuming that the gas fills the entire cavity, the decay time becomes:
      τ    =                  n        c            ·              l                  1          -          R          +          X          +                      α            ⁢                                                  ⁢            l                                ,where α is the absorption coefficient of specific gas tested. This is called a linear approximation as a is considered independent of the intensity of the radiation.
In other words, the cavity ring-down event occurs by abruptly stopping the radiation from the laser that impinges on the cavity and is characterized by a power transmitted which decays according to the exponential function exp(−γt), where γ=1/τ and t is the time measured from the moment of interruption of the incident wave.
If the cavity has an internal linear absorbing medium, the constant γ is simply the sum of two terms: γc representing the empty cavity contribution and γg which represents that of the medium absorption. With two measures, one with empty cavity and one with absorbent medium, the value of γg can therefore be ideally determined.
Recently, a new technique was presented related to laser spectroscopy, called “saturated-absorption cavity ring-down spectroscopy” (hereinafter briefly SCAR), described in “Saturated-absorption cavity ring-down spectroscopy” written by G. Giusfredi et al., Phys. Rev. Lett. 104, 110801 (2010), which has proven that high sensitivity can be achieved. This technique is called below ring-down spectroscopy under saturation of absorption. This means that the intensity of light radiation in the cavity that is set is much greater than the saturation intensity of the molecular transition to detect.
SCAR spectroscopy uses a non-linear model bringing the absorbing medium to saturation, i.e. the intensity of the laser beam is such as to lead the molecular transition of the gas of interest—resonant with the laser—to saturation. In other words, the wavelength of the electromagnetic radiation emitted by the laser is adjusted so that it is in resonance with the transition of interest and the intensity of the radiation itself is increased or adjusted so that this transition is brought to a saturation condition. From the studies reported by the Applicants, they have figured out how to take advantage of the fact that a cavity containing a gas in high saturation conditions behaves almost as a empty cavity in relation to radiation, i.e. when the laser is switched off, the emission of photons follows a curve similar to that of the empty cavity at least for a first time interval. This scheme is called “effective empty cavity scheme”. Therefore, in an experiment where saturation is reached inside the cavity using a beam having a sufficient intensity and then turning off the same, measuring the radiation emitted with a photodetector, a curve is obtained that for a first part follows the decay pattern in an empty cavity. After a certain period of time, however, the behavior of the radiation emitted is no longer that of an empty cavity, since many photons have already left the cavity that contains a gas that is no longer under saturation conditions, thus for a second time interval the decay curve is the curve that one would get if the cavity was filled by a non-saturated gas, i.e., one gets back to the linear scheme. Thus, by measuring the radiation emitted by the cavity, the two decays are measured together, using both the saturation condition and the linear condition, and thus they may be subtracted in order to obtain the decay due solely to the gas in the cavity.
In this way it is possible to obtain both the contribution γc of the empty cavity and that γg of the gas under linear absorption at low intensity from the same decay event. In other words, the value of γg is encoded in the deformation of exponential decay. Since in principle all information to be obtained is contained in the same decay event, the SCAR spectroscopy minimizes the following errors that are introduced in the measures and cause not to be in an ideal condition, essentially preventing two measures as in conventional CDR spectroscopy:                the non-monochrome condition of the wave emitted by the laser which is incident inside the cavity;        the imperfect immediacy of the interruption of the wave to be “turned off” to measure the ring-down time;        the fluctuations of the resonant frequency of the cavity;        the imperfect adaptation of the spatial mode of the incident wave produced by the laser with the cavity mode, which can also vary over time;        the reflectivity unevenness of the mirrors forming the cavity, which combines with the alignment fluctuations of the incident wave;        the dependence of γc on frequency, if to go from “full cavity” to “empty cavity” different longitudinal resonant modes of the cavity are used, one coincident with a region of absorption of the medium (i.e. the gas introduced into the cavity the concentration of which is to be measured) and one in a region of transparency;        the fluctuation of this dependency over time.        
To give a quantitative idea of the resolution obtainable through the SCAR technique, consider the special case of radiocarbon dioxide detection in natural abundance. In optimum conditions of temperature and pressure, the deformation from a pure exponential produced by radiocarbon along decay signals is of the order of 1 μV on 3 V. This places very stringent limits on the residual non-linearity which can be borne.
The measurement is possible thanks to the noise present in the signal to be captured, which in good approximation has no or at least constant average. By mediating many events (each decay signal deposited in memory is the average of 1280 events), it is possible to increase the resolution of digitisation by approximately 35 times.